WEBVTT 00:00:00.040 --> 00:00:02.819 Hi, yesterday we talked about the courage it 00:00:02.819 --> 00:00:06.179 takes to step into a difficult conversation by 00:00:06.179 --> 00:00:09.099 suggesting different starting points. But what 00:00:09.099 --> 00:00:12.880 happens when we do not speak up? What happens 00:00:12.880 --> 00:00:15.619 if we do not follow through on our intuitions? 00:00:15.880 --> 00:00:20.260 What if we ignore our curious doubts? What if 00:00:20.260 --> 00:00:25.000 we just let certainty rule the day? From my experience, 00:00:25.160 --> 00:00:28.019 when I ignore my questions and let certainty 00:00:28.019 --> 00:00:32.229 be the only voice, I can feel my mind close. 00:00:33.469 --> 00:00:38.590 Oxygen gets sucked up. Of course, certainty is 00:00:38.590 --> 00:00:41.969 not always bad. In math, certainty feels powerful. 00:00:42.250 --> 00:00:45.969 Once something is proven, it is settled. And 00:00:45.969 --> 00:00:49.609 that clarity is beautiful. But we've learned 00:00:49.609 --> 00:00:52.990 that math also reminds us there is more to the 00:00:52.990 --> 00:00:57.689 story on certainty. Every result depends on where 00:00:57.689 --> 00:01:01.159 we start. And when that starting point changes, 00:01:01.539 --> 00:01:06.400 a different, yet still logical, result can appear. 00:01:06.599 --> 00:01:12.200 The surprise is not error. The surprise is expansion. 00:01:12.959 --> 00:01:16.280 We saw that in geometry when we changed the parallel 00:01:16.280 --> 00:01:19.760 postulate. This is not just an isolated example. 00:01:20.260 --> 00:01:23.780 Math has evolved by constantly changing starting 00:01:23.780 --> 00:01:28.219 points. Here's more of an algebra example. For 00:01:28.219 --> 00:01:30.920 a long time, mathematicians believed that every 00:01:30.920 --> 00:01:34.540 number, when squared, must be positive. That 00:01:34.540 --> 00:01:38.700 seems obvious, until someone asked, what if we 00:01:38.700 --> 00:01:42.099 allow a number whose square is negative? Call 00:01:42.099 --> 00:01:47.099 it i, where i squared equals negative 1. Well, 00:01:47.099 --> 00:01:50.799 at first, it sounds impossible. But once that 00:01:50.799 --> 00:01:54.900 idea is accepted, an entirely new system opens 00:01:54.900 --> 00:01:59.340 up. It does not replace what came before. It 00:01:59.340 --> 00:02:03.819 expands it. It did not just expand algebra. It 00:02:03.819 --> 00:02:06.980 expanded our number system. It created another 00:02:06.980 --> 00:02:12.599 new world to do math. The complex plane. The 00:02:12.599 --> 00:02:15.979 original system was not wrong. It just was not 00:02:15.979 --> 00:02:20.520 complete. So what does this mean beyond math? 00:02:21.710 --> 00:02:23.830 Certainty does not just show up in equations. 00:02:24.030 --> 00:02:27.250 It shows up in how I see the world. And when 00:02:27.250 --> 00:02:29.990 I look back on my life, I notice my thinking 00:02:29.990 --> 00:02:33.490 begins to shrink when I assume my perspective 00:02:33.490 --> 00:02:37.389 is the correct perspective. I close the door 00:02:37.389 --> 00:02:41.430 to possibilities I cannot yet imagine. To ideas 00:02:41.430 --> 00:02:45.189 that do not seem possible, at least from where 00:02:45.189 --> 00:02:48.849 I'm standing. But math tells a different story. 00:02:49.520 --> 00:02:53.639 Math is a history of expanding what we once thought 00:02:53.639 --> 00:02:59.000 was impossible. And doing math invites a different 00:02:59.000 --> 00:03:04.419 posture to keep exploring, keep asking, keep 00:03:04.419 --> 00:03:10.039 listening. It invites us to sit in tension, not 00:03:10.039 --> 00:03:14.780 to avoid it. Yes, certainty can give clarity, 00:03:14.900 --> 00:03:19.439 but it can also limit what I'm able to see. And 00:03:19.439 --> 00:03:23.960 when I begin to notice that, I realize the way 00:03:23.960 --> 00:03:28.280 I see the world is not just about the world. 00:03:28.740 --> 00:03:35.560 It is shaped by how I've learned to think. So 00:03:35.560 --> 00:03:38.740 my questions today are, where might my certainty 00:03:38.740 --> 00:03:42.939 be closing my mind? What assumptions am I holding 00:03:42.939 --> 00:03:46.319 onto that are keeping me from seeing something 00:03:46.319 --> 00:03:50.520 more? something bigger, something more beautiful.